Moving Coil Meters
The design of a
voltmeter,
ammeter or
ohmmeter
begins with a current-sensitive element. Though most modern meters have
solid state digital readouts, the physics is more readily demonstrated
with a moving coil current detector called a
galvanometer.
Since the modifications of the current sensor are compact, it is
practical to have all three functions in a single instrument with
multiple ranges of sensitivity. Schematically, a single range
"multimeter" might be designed as illustrated.

Voltmeter
A voltmeter measures the change in voltage
between two points in an electric circuit and therefore must be
connected in parallel with the portion of the circuit on which the
measurement is made. By contrast, an ammeter must be connected in series. In analogy with a water circuit,
a voltmeter is like a meter designed to measure pressure difference. It
is necessary for the voltmeter to have a very high resistance so that
it does not have an appreciable affect on the current or voltage
associated with the measured circuit. Modern solid-state meters have
digital readouts, but the principles of operation can be better
appreciated by examining the older moving coil meters based on galvanometer sensors.

Ammeter
An ammeter is an instrument for measuring the electric current
in amperes in a branch of an electric circuit. It must be placed in
series with the measured branch, and must have very low resistance to
avoid significant alteration of the current it is to measure. By
contrast, an voltmeter must be connected in parallel. The analogy with an in-line flowmeter in a water circuit
can help visualize why an ammeter must have a low resistance, and why
connecting an ammeter in parallel can damage the meter. Modern
solid-state meters have digital readouts, but the principles of
operation can be better appreciated by examining the older moving coil meters based on galvanometer sensors.

Ohmmeter
The standard way to measure resistance in ohms is to supply a
constant voltage to the resistance and measure the current through it.
That current is of course inversely proportional to the resistance
according to Ohm's law,
so that you have a non-linear scale. The current registered by the
current sensing element is proportional to 1/R, so that a large current
implies a small resistance. Modern solid-state meters have digital
readouts, but the principles of operation can be better appreciated by
examining the older moving coil meters based on galvanometer sensors.

Voltmeter/Ammeter Measurements
The value of electrical resistance associated with a circuit
element or appliance can be determined by measuring the voltage across
it with a voltmeter and the current through it with an ammeter and then dividing the measured voltage by the current. This is an application of Ohm's law,
but this method works even for non-ohmic resistances where the
resistance might depend upon the current. At least in those cases it
gives you the effective resistance in ohms under that specific
combination of voltage and current.
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